How do anthropologists know whether skeletons of ancient humans were male or female?

Ancient humans knew they were male or female and stayed that way.

There are several ways.  The easiest to see if the pelvis of a female is much more open for childbirth.  But you can tell even from just a skull.

your rant is noted

Adult emales have wider hips than adult males . There is also DNA and chemical.analysis, 

 Sometimes more than one person's bones are are used to make a skeleton.  

Don't project and transfer your ignorance onto other people. 

Pelvis and brow ridge difference

But I'm sure a very few are wrong but why does that matter

Biology fail.......

Females hip bones are much different than males. 

That depends.

For non Christian anthropologists they examine the pelvis and skull.

Christian anthopologists count the ribs, then give up because both sexes have the same number. It is at this point they hand it over to real scientists.

A skeleton's overall size and sturdiness give some clues. Within the same population, males tend to have larger, more robust bones and joint surfaces, and more bone development at muscle attachment sites. However, the pelvis is the best sex-related skeletal indicator, because of distinct features adapted for childbearing. The skull also has features that can indicate sex, though slightly less reliably.